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%I #11 May 13 2013 01:50:00
%S 3,1,4,2,6,6,2,7,4,7,3,5,9,7,0,3,5,1,7,9,1,8,2,9,8,9,3,3,1,1,8,3,8,7,
%T 3,1,8,3,2,7,5,9,3,6,5,9,2,2,2,5,9,0,2,0,4,6,4,8,0,5,4,6,2,7,0,7,4,7,
%U 0,9,7,7,3,6,1,0,6,3,5,3,3,9,5,6,1,0,6,3,8,4,5,1,4,1,6,1,6,9,5,8,2,5,7,2,1
%N Decimal expansion of sqrt(phi) / (1 - phi/e) where phi=(1+sqrt(5))/2.
%C Sqrt(phi) / (1 - phi/e) is somewhat close to Pi.
%C Because phi/e < 1 we have sqrt(phi) / (1 - phi/e) = sqrt(phi) * Sum_{n=0..Infinity}( phi/e) ^n. We obtain a better approximation of Pi with 14 terms: sqrt(phi) * Sum_{n=0..14} ( phi/e) ^n = 3.14135146821891366128707....
%e 3.14266274735970351791829....
%t RealDigits[N[Sqrt[GoldenRatio]/(1-GoldenRatio/E),105]]
%o (PARI) phi=(1+sqrt(5))/2;sqrt(phi)/(1-phi/exp(1)) \\ _Charles R Greathouse IV_, Dec 28 2011
%Y Cf. A001113.
%K nonn,cons
%O 1,1
%A _Michel Lagneau_, Dec 13 2011
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